| Title:
|
Homogenized double porosity models for poro-elastic media with interfacial flow barrier (English) |
| Author:
|
Ainouz, Abdelhamid |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
357-365 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper a Barenblatt-Biot consolidation model for flows in periodic porous elastic media is derived by means of the two-scale convergence technique. Starting with the fluid flow of a slightly compressible viscous fluid through a two-component poro-elastic medium separated by a periodic interfacial barrier, described by the Biot model of consolidation with the Deresiewicz-Skalak interface boundary condition and assuming that the period is too small compared with the size of the medium, the limiting behavior of the coupled deformation-pressure is studied. (English) |
| Keyword:
|
homogenization |
| Keyword:
|
porelasticity |
| Keyword:
|
two-scale convergence |
| MSC:
|
35B27 |
| MSC:
|
35Q35 |
| MSC:
|
74Q05 |
| MSC:
|
76M50 |
| idZBL:
|
Zbl 1249.35016 |
| idMR:
|
MR2985545 |
| DOI:
|
10.21136/MB.2011.141695 |
| . |
| Date available:
|
2011-11-10T15:48:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141695 |
| . |
| Reference:
|
[1] Ainouz, A.: Derivation of a convection process in a steady diffusion-transfer problem by homogenization.Int. J. Appl. Math. 21 (2008), 83-97. Zbl 1144.35329, MR 2408055 |
| Reference:
|
[2] Allaire, G.: Homogenization and two-scale convergence.SIAM J. Math. Anal. 23 (1992), 1482-15192. Zbl 0770.35005, MR 1185639, 10.1137/0523084 |
| Reference:
|
[3] Allaire, G., Damlamian, A., Hornung, U.: Two scale convergence on periodic surfaces and applications.Proceedings of the International Conference on Mathematical Modelling of Flow through Porous Media (May 1995) A. Bourgeat et al. (1996), 15-25 World Scientific Singapore. |
| Reference:
|
[4] Barenblatt, G., Zheltov, Y., Kochina, I.: On basic concepts of the theory of homogeneous fluids seepage in fractured rocks.Russian Prikl. Mat. Mekh. 24 (1960), 852-864. |
| Reference:
|
[5] Biot, M.: General theory of the three-dimensional consolidation.J. Appl. Physics 12 (1941), 155-164. 10.1063/1.1712886 |
| Reference:
|
[6] Biot, M., Willis, D.: The elasticity coefficients of the theory of consolidation.J. Appl. Mech. 24 (1957), 594-601. MR 0092472 |
| Reference:
|
[7] Deresiewicz, H., Skalak, R.: On uniqueness in dynamic poroelasicity.Bull. Seismol. Soc. Amer. 53 (1963), 783-788. |
| Reference:
|
[8] Ene, H., Poliševski, D.: Model of diffusion in partially fissured media.Z. Angew. Math. Phys. 53 (2002), 1052-1059. Zbl 1017.35016, MR 1963553, 10.1007/PL00013849 |
| Reference:
|
[9] Showalter, R., Momken, B.: Single-phase flow in composite poroelastic media.Math. Methods Appl. Sci. 25 (2002), 115-139. Zbl 1097.35067, MR 1879654, 10.1002/mma.276 |
| Reference:
|
[10] Wilson, R., Aifantis, E.: On the theory of consolidation with double porosity.Int. J. Eng. Sci. 20 (1982), 1009-1035. Zbl 0493.76094, 10.1016/0020-7225(82)90036-2 |
| . |
